       Re: Converting the integral of a sum into a sum of integrals

• To: mathgroup at smc.vnet.net
• Subject: [mg109147] Re: Converting the integral of a sum into a sum of integrals
• From: Roland Franzius <roland.franzius at uos.de>
• Date: Mon, 19 Apr 2010 04:11:37 -0400 (EDT)
• References: <201004110831.EAA06714@smc.vnet.net> <hputps\$lhj\$1@smc.vnet.net>

```Kurt TeKolste schrieb:
> If I ask Mathematica to perform an indefinite integrate on a symbolic
> summation (with terms of the form a_i x^i),
>
> Integrate[Sum[Times[Power[x,i],Subscript[a,i]],{i,0,k}],
>
> it does nothing.  If I try to tell it that summation and integration
> commute by applying the rule:
>
> Integrate[Sum[term_,range_],variable_]->
> Sum[Integrate[term_,variable_],range_]
>
> I get a strange result equivalent to
>
> term * range

meaning that Integrate does not see term dependent on variable

>
> or, in this case,
>
> Times[Power[x,i],Subscript[a,i]] * {i,0,k}
> or
> {i a_i x^i, 0, k a_i x^i}
>
> Any ideas as to what's going on?
>
> (BTW:
>
> 1)  If you use rules to extract each of term, range, and variable and
> then take Sum[Integral[...],...] the correct answer is returned.
>
> 2)  if you use a rule that changes Sum to Power, i.e.
>
> Integrate[Sum[term_,range_],variable_] ->
> Product[Integrate[term_,variable_],range_]
>
> you get exponents
>
> term^(range - 1)
>
> Odd...
> )
>
> ekt
>

Use rules that hold its pattern form unevaluated. HoldPattern preserves
execution of the first argument of RuleDelayed at any stage of the
defining or execution process.

Using RuleDelayed (:> )instead of Rule (->) delays evaluation of its
second argument to the time of applying the rule in a Replace (/.)

--

Roland Franzius
rule = HoldPattern[Integrate[Sum[expression_,j_],x_] :>
Sum[Integrate[expression,x],j]

```

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